While these modelling approaches are well-suited for the study of subsonic or ideally expanded supersonic jets, their applicability to shock-containing flows is less straightforward. As summarised in recent reviews [1]}, [2]}, these flows are usually subject to a resonance phenomenon called screech, which leads to the appearance of sharp tones in the acoustic fields of imperfectly expanded jets. As shown recently by [3]}, this phenomenon is caused by an absolute instability mechanism triggered by the flow periodicity induced by the shock-cells, which causes disturbances to grow in both space and time until they reach a saturated state. This absolute instability leads to unstable global modes, as shown in [4]} (or marginally stable ones, as in [5]}). The high computational cost associated with computing global modes in these flows limits their utility for wavepacket modelling. The presence of sharp discontinuities in the flow prohibits the application of PSE and other WKB-based methods as well. As shown by [6]}, the PSE approach is only beneficial when the flow properties are slowly varying in the streamwise direction, and when the flow is only convectively unstable (no absolute instability); none of these conditions are satisfied in shock-containing jets. For that reason, most of the broadband shock-associated noise (BBSAN) prediction models are based either on first principles (as in [7]}, [8]}, [9]}) or numerical simulations [10]}, [11]}. As the key mechanism of this phenomenon is the interaction between instability waves and the shock-cell structure, a low-order model for predicting the equivalent shock-modulated wavepacket for these jets would be useful.
